So my question is, is that right or is it anachronic? I mean, were the Romans aware that the Sun shone in other places during the night? I know that in the Middle Ages they thought the Earth was flat, but what was it like in their times?

In a way, Greeks and Romans were aware, that the earth was round. By studying ships and how they disappear in the horizon, and from the shadows in the Pyramids, they managed to calculate earth's radius, quite precisely for that time. Traditionally it's said, Eratosthenes was the first one to do this, and Thales may have calculated sun's distance from the earth. But these ideas (that the earth is a globe) were not accepted by the majority of philosophers. Later these ideas faded, the "flat earth" theory prevailed, and at late medieval coexisted with other theories like the flat earth.

loqu wrote:I know that in the Middle Ages they thought the Earth was flat, but what was it like in their times?

An educated Roman would absolutely know about the earth being round, and also be able to correctly explain such phenomena as lunar eclipses. And, contrary to what many believe, this view never ceased to be commonly accepted, even in medieval times. (This is amongst the educated, of course; if you had no experience of the world outside your own little town, you might of course have any or no conception about the form of the earth. But I think it is fair to say that, if you were able to read, you would have been, at the very very least, exposed to the idea of a spherical earth.)

Edit: That is, there were never any real dissention concerning the spherical earth theory in the Middle Age; this should of course not be confused with two other related concept, about which there was a genuine debate, namely 1) whether or not humans could live on the other half of the earth, below the equator, and 2) whether the earth revolved around the sun, or vice versa.

loqu wrote:I know that in the Middle Ages they thought the Earth was flat

Anyone who reads Dante (written in the early 1300's) knows that the concept of a spherical earth was commonly accepted by then. He and Virgil travel through the center of the spherical earth and even flip over as they cross the very center of the earth because the force of gravity is going the other way. On the other side of the earth they find the island a Purgatory, a place to where Odysseus had previously sailed, we learn. So Dante certainly believed the earth was a sphere and he certainly expected that anyone reading his story would have thought so, too.

I know that in the Middle Ages they thought the Earth was flat, but what was it like in their times?

that is incorrect, the debate came to be about the sun revolving around the earth or the earth revolving around the sun... both of which already assume the earth to be a sphere. it is a common historical misconception.